Finding an optimal path without growing the tree

For problems on computing an optimal path as well as its length in a certain setting, the “standard” approach for finding an actual optimal path is by building (or “growing”) a single-source optimal path tree. In this paper, we study a class of optimal path problems with the following phenomenon: Th...

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Vydáno v:Journal of algorithms Ročník 49; číslo 1; s. 13 - 41
Hlavní autoři: Chen, Danny Z., Daescu, Ovidiu, Hu, Xiaobo (Sharon), Xu, Jinhui
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: San Diego, CA Elsevier Inc 01.10.2003
Elsevier
Témata:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Arrangements
Combinatorics
Combinatorics. Ordered structures
Computational geometry
Computer science; control theory; systems
Convex and discrete geometry
Dynamic programming
Exact sciences and technology
Geometry
Graph theory
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Optimal paths
Sciences and techniques of general use
Space-efficient algorithms
Theoretical computing
Arrangements
Computational geometry
Optimal paths
Space-efficient algorithms
Dynamic programming
Tree data structures
Computer theory
Shortest path
Scheduling
Combinatorial optimization
Arrangement
Knapsack problem
Space-efficient algorithm
Space complexity
Algorithm complexity
Optimal path
ISSN:0196-6774, 1090-2678
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Popis
Shrnutí:For problems on computing an optimal path as well as its length in a certain setting, the “standard” approach for finding an actual optimal path is by building (or “growing”) a single-source optimal path tree. In this paper, we study a class of optimal path problems with the following phenomenon: The space complexity of the algorithms for reporting the lengths of single-source optimal paths for these problems is asymptotically smaller than the space complexity of the “standard” tree-growing algorithms for finding actual optimal paths. We present a general and efficient algorithmic paradigm for finding an actual optimal path for such problems without having to grow a single-source optimal path tree. Our paradigm is based on the “marriage-before-conquer” strategy, the prune-and-search technique, and a new data structure called clipped trees. The paradigm enables us to compute an actual path for a number of optimal path problems and dynamic programming problems in computational geometry, graph theory, and combinatorial optimization. Our algorithmic solutions improve the space bounds (in certain cases, the time bounds as well) of the previously best known algorithms, and settle some open problems. Our techniques are likely to be applicable to other problems.
ISSN:0196-6774
1090-2678
DOI:10.1016/S0196-6774(03)00080-4